Solved – Which performance metrics for highly imbalanced multiclass dataset

aucclassificationmodel-evaluationprecision-recallunbalanced-classes

I have a dataset with 5 classes. About 98% of the dataset belong to class 5. Classes 1-4 share equally about 2% of the dataset. However, it is highly important, that classes 1-4 are correctly classified.

The accuracy is not a good measure of performance for my task. I found lots of information on metrics for imbalanced binary classification tasks but not on multiclass problems.

Which performance metrics should I use for such a task?

  • TP, TN, FP, FN
  • Precision
  • Sensitivity
  • Specificity
  • F-score
  • ROC-AUC (micro, macro, samples, weighted)

Best Answer

For unbalanced classes, I would suggest to go with Weighted F1-Score or Average AUC/Weighted AUC

Let's first see F1-Score for binary classification.

The F1-score gives a larger weight to lower numbers.

For example,

  • when Precision is 100% and Recall is 0%, the F1-score will be 0%, not 50%.
  • When let us say, we have Classifier A with precision=recall=80%, and Classifier B has precision=60%, recall=100%. Arithmetically, the mean of the precision and recall is the same for both models. But when we use F1’s harmonic mean formula, the score for Classifier A will be 80%, and for Classifier B it will be only 75%. Model B’s low precision score pulled down its F1-score.

Now, come to the Mutliclass Classification

Let us suppose we have the five classes, class_1, class_2, class_3, class_4, class_5

and the model is having the following results for each class.

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forula for precision for each class = (True Positive for class)/(Count of predicted Positive for that class)

e.g. precision for class_1 = (True Positive for class_1)/(Count of Predicted of class_1)

forula for Recall for each class = (True Positive for class)/(Actual Positive for that class)

e.g. precision for class_1 = (True Positive for class_1)/(Total instances of class_1)

Formula for F1: F1 is the geometric mean of Precision and Recall i.e.

F1 = 2*(Precision*Recall)/(Precision+Recall)

Macro-F1 = Average(Class_1_F1 + Class_2_F1 + Class_3_F1 + Class_4_F1 + Class_5_F1)

Macro-Precision = Average(Class_1_Precision + Class_2_Precision + Class_3_Precision + Class_4_Precision + Class_5_Precision)

Macro-Recall = Average(Class_1_Recall + Class_2_Recall + Class_3_Recall + Class_4_Recall + Class_5_Recall)

Problem with Macro calculation: When averaging the macro-F1, we gave equal weights to each class.

Weighted F1 Score:

We don’t have to do that: in weighted-average F1-score, or weighted-F1, we weight the F1-score of each class by the number of samples from that class. 

Weighted F1 Score = (N1*Class_1_F1 + N2*Class_2_F1 + N3*Class_3_F1 + N4*Class_4_F1 + N5*Class_5_F1)/(N1 + N2 + N3 + N4 + N5)

References: https://towardsdatascience.com/multi-class-metrics-made-simple-part-ii-the-f1-score-ebe8b2c2ca1

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